-LRB- CNN -RRB- -- The Sudanese president has vowed to `` never give up '' a disputed oil-rich region that has escalated tensions with South Sudan and sparked fears of the two neighbors ' return to war .

Clashes between the two nations soared in the past week after South Sudan declared the disputed Heglig region is under its control .

Sudan also claims ownership and has lodged complaints with the United Nations and the African Union , urging them to pressure South Sudan to withdraw troops from its territory .

The United States on Thursday called for both sides to stop the hostilities .

`` We condemn South Sudan 's military involvement in the attack on and seizure of Heglig , an act which goes beyond self-defense and has increased tensions between Sudan and South Sudan to dangerous levels , '' State Department spokeswoman Victoria Nuland said . `` We also condemn the continued aerial bombardment in South Sudan by the Sudanese Armed Forces . ''

U.N. Secretary-General Ban Ki-moon urged both countries to return to the negotiating table .

`` The last thing the people of these two countries need is another war -- a war that could claim countless lives , destroy hope and ruin the prospects of peace and stability and prosperity of all Sudanese people , '' he said .

China , which has invested heavily Sudan 's oil industry , also argued for calm .

`` China again calls for the two countries to immediately stop hostility and respect each other 's sovereignty , '' Liu Weiming , a spokesman for the Chinese Ministry of Foreign Affairs , said at a regular news briefing Thursday .

During a rally broadcast on state media , Sudanese President Omar al-Bashir said , `` We will never give up an inch of our land . And we have said it before , whoever extends his hand toward Sudan , we will cut it off . ''

The international community has urged Sudan and South Sudan to return to the table amid intensified tensions . South Sudan split from its neighbor in July under the terms of a 2005 peace agreement that ended decades of a civil war .

During the defiant speech , the Sudanese leader told citizens that `` Heglig is in Kordofan , '' referring to a border state owned by the nation .

`` We will punish them ... and it will be the last lesson for them , '' he said . `` If they do not understand , we will make them get it by force . We extended our hand before for peace and unity . But they deceived us . Heglig is the start . ''

South Sudan did not immediately respond to the latest speech , but a military official vowed to retain a grip on the region a day earlier .

`` We will hold this position , '' said Maj. Gen. Mangar Buong , a deputy commander for the South Sudanese military .

Princeton Lyman , the U.S. Special Envoy for Sudan and South Sudan , has been in both countries recently , holding meetings with government officials .

There is `` an enormous amount of very emotional , very powerful rhetoric coming from here in Khartoum raising the stakes in many ways and that 's worrisome in and of itself , '' he said on a conference call from Khartoum on Thursday .

But he said that based on the discussions he 'd had in both Khartoum and Juba , `` I can say with confidence that virtually everyone I have talked to has said , ` Look , we do n't want to go to all out war with the other , we need to find a way out . ' ''

Tensions run deep between the two nations , which have outstanding issues despite their divorce last year .

Unresolved issues include status of citizens , how much the landlocked South should pay to transport its oil through Sudan and the division of national debt , among others . The fate of disputed border areas is also a point of contention .

As long-simmering tensions soar , rights group are warning of deteriorating humanitarian conditions .

`` The deteriorating situation right now is making the overall humanitarian issues very challenging , '' said Alex Neve , secretary-general of Amnesty International Canada .

Neve , who is in the South Sudan capital of Juba , said supply lines at refugee camps have been cut off and failure to get key supplies before the rains will lead to a humanitarian crisis .

In addition , there are reports of human rights violations .

`` The refugees coming in across the border have consistent stories of aerial bombardments and ground attacks '' from Sudanese soldiers , he said .

CNN 's Amir Ahmed , David McKenzie , Faith Karimi and Jamie Crawford contributed to this report .

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NEW : U.S. envoy says both sides want to avoid war despite rhetoric

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China and the U.N. call for an end to hostilities by both sides

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Clashes between the two nations soar in the past week

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Tensions intensified after South Sudan said it seized the disputed Heglig region